A259673 a(n) = sigma_(prime(n))(n).

1, 9, 244, 16513, 48828126, 13062296532, 232630513987208, 144115462954287105, 8862938119746644274757, 100000000186264514923632574038, 191943424957750480504146841291812, 8505622499882988712256991112913772434548, 4695452425098908797088971409337422035076128814

Offset: 1

Author

Ilya Gutkovskiy, Jul 03 2015

Keywords

• nonn
• easy

Links

• Anders Hellström, Table of n, a(n) for n = 1..50
• Index entries for sequences related to sums of divisors

Crossrefs

Cf. A000203 (sigma(n)), A000040 (prime(n)), A023887 (sigma_n(n)).

Cf. A001157 (sigma_2), A001158 (sigma_3), A001160 (sigma_5), A013955 (sigma_7).

Programs

Magma

[DivisorSigma(NthPrime(n),n):n in [1..15]]; // Vincenzo Librandi, Jul 15 2015

Maple

a:= n-> numtheory[sigma][ithprime(n)](n):
seq(a(n), n=1..15);  # Alois P. Heinz, Feb 10 2020

Mathematica

a[n_] := DivisorSigma[Prime[n], n]; Array[a, 13]
(* Second program: *)
a[n_] := SeriesCoefficient[Sum[k^Prime[n]*x^k/(1-x^k), {k, 1, n}], {x, 0, n}]; Array[a, 13] (* Jean-François Alcover, Sep 29 2017, from 2nd formula *)

PARI

a(n) = sigma(n, prime(n)); \\ Michel Marcus, Jul 03 2015

Python

from sympy import divisor_sigma, prime
def A259673(n):
    return divisor_sigma(n,prime(n)) # Chai Wah Wu, Jul 20 2015

Formula

a(n) = sigma_(A000040(n))(n).

a(n) = [x^n] Sum_{k>=1} k^prime(n)*x^k/(1 - x^k). - Ilya Gutkovskiy, Sep 26 2017

Extensions

a(11) and a(12) from Anders Hellström, Jul 14 2015